323,077 research outputs found
Beyond Regular Semigroups
No full textThe topic of this thesis is the class of weakly U-abundant semigroups. This class is very wide, containing inverse, orthodox, regular, ample, adequate, quasi-adequate, concordant, abundant, restriction, Ehresmann and weakly
abundant semigroups. A semigroup with subset of idempotents U is weakly U-abundant if every \art_U-class and every \elt_U-class contains an idempotent of U, where \art_U and \elt_U are relations extending the well known Green's relations \ar and \el. We assume throughout that our semigroups satisfy a condition known as the Congruence Condition (C).
We take several approaches to weakly -abundant semigroups. Our first results describe those that are analogous to completely simple semigroups. Together with an existing result of Ren this determines the structure of those weakly -abundant semigroups that are analogues of completely regular semigroups, that is, they are superabundant. Our description is in terms of a semilattice of rectangular bands of monoids.
The second strand is to aim for an extension of the Hall-Yamada theorem for orthodox semigroups as spined products of inverse semigroups and fundamental orthodox semigroups. To this end we consider weakly -orthodox semigroups, where is a band. We note that if
is a semilattice then a weakly -orthodox semigroup is exactly an Ehresmann semigroup. We provide a description of a weakly -orthodox semigroup as a spined product of a fundamental weakly -orthodox semigroup (depending only on ) and , where is isomorphic to and is the analogue of the least inverse congruence on an orthodox semigroup. This result is an analogue of the Hall-Yamada theorem for orthodox semigroups. In the case that is a normal band, or is weakly -superabundant, we find a closed form for , which simplifies our result to a straightforward form.
For the above to work smoothly in the case is weakly -superabundant, we need to find a canonical fundamental weakly -superabundant subsemigroup of . This we do, and give the corresponding answers in the case of the Hall semigroup and a number of intervening semigroups.
We then change our direction. A celebrated result of Nambooripad shows that regular semigroups are determined by ordered groupoids built over a regular biordered set. Our aim, achieved at the end of the thesis, is to extend Nambooripad's work to {\em weakly -regular}
semigroups, that is, weakly -abundant semigroups with (C) and generating a regular subsemigroup
whose set of idempotents is .
As an intervening step we consider weakly -orthodox semigroups in this light. We take two approaches. The first is via a new construction of an inductive generalised category over a band. In doing so we produce a new approach to characterising orthodox semigroups, by using inductive generalised groupoids.
We show that the category of weakly -orthodox semigroups is isomorphic to the category of inductive generalised categories over bands. Our approach is influenced by that of Nambooripad, however, there are significant differences in strategy, the first
being the introduction of generalised categories and the second being that it is more convenient to consider (generalised) categories equipped with pre-orders, rather than with partial orders. Our work may be regarded as extending a result of Lawson for Ehresmann semigroups. We also examine the trace of a weakly -orthodox semigroup, which is a primitive weakly -orthodox semigroup.
We then take a more `traditional' approach to weakly -orthodox semigroups via band categories and weakly orthodox categories over a band, equipped with two pre-orders. We show that the category of weakly -orthodox semigroups is equivalent to the category of weakly orthodox categories over bands. To do so we must substantially adjust Armstrong's method for concordant semigroups.
Finally, we consider the most general case of weakly -regular semigroups. Following Nambooripad's theorem, which establishes a correspondence between algebraic structures (inverse semigroups) and ordered structures (inductive group-oids), we build a correspondence between the category of weakly -regular semigroups and the category of weakly regular categories over regular biordered sets, equipped with two pre-orders
Hopf-Galois extensions and twisted Hopf algebroids
No full textWe show that the Ehresmann-Schauenburg bialgebroid of a quantum principal bundle P or Hopf Galois extension with structure quantum group H is in fact a left Hopf algebroid L(P,H). We show further that if H is coquasitriangular then...We propose a new notion of antipode S for a left Hopf algebroid which does not assume antimultipicativity. We also show that if..
Déformations conformes des variétés de Finsler-Ehresmann
No full textAn intrinsic approach to Finsler geometry is proposed. A concept of Finsler- Ehresmann manifold, denoted by (M,F,H), is introduced and a generalized Chern connection is built for this manifold. Conformal deformations on this manifold are considered. First, we have an analogous of Chern's theorem: we prove the existence and uniqueness of a generalized Chern connection for the manifold (M,F,H). Similarly, within an essentially koszulian formalism, we present two curvatures associated to this generalized connection, namely a R curvature and a P one. The second result is the deduction of conformal transformations laws for the generalized Chern connection and associated curvatures. The transformation of R seems to have very similar properties as that of the Riemannian curvature while that of P reveals other objects of pure Finslerian nature. Third, we construct the finsler Weyl and Schouten tensors W and S respectively and we study their conformal transformations. Furthermore, we show that for the dimension 3, the horizontal component of W for generalized Berwald manifolds is identically zero. The next result is a theorem of Weyl-Schouten type giving necessary and sufficient conditions for a Finsler-Ehresmann manifold to be conformaly R-flat. We complete this result by exploring the case of dimension 3 for Berwald spaces which gives a result very similar to the Riemannian case. In addition, we announce some necessary conditions to characterize conformal flatness of Finsler-Ehresmann manifolds.GR-T
Characteristic classes and Ehresmann connections for Legendrian foliations
No full textAbstract. We find a necessary and sufficient condition for the (local) projectabil-
ity of a Legendrian foliation of an almost S-manifold onto a Lagrangian foliation of a
symplectic manifold. In the context of Legendrian foliations, this result will be used
for proving a Darboux theorem and some results about primary and secondary char-
acteristic classes. Finally we show that, under suitable assumptions, every Legendrian
foliation admits an Ehresmann connection
LEFT ADEQUATE AND LEFT EHRESMANN MONOIDS
No full text This is the first of two articles studying the structure of left adequate and, more generally, of left Ehresmann monoids. Motivated by a careful analysis of normal forms, we introduce here a concept of proper for a left adequate monoid M. In fact, our notion is that of T-proper, where T is a submonoid of M. We show that any left adequate monoid M has an X*-proper cover for some set X, that is, there is a left adequate monoid [Formula: see text] that is X*-proper, and an idempotent separating surjective morphism [Formula: see text] of the appropriate type. Given this result, we may deduce that the free left adequate monoid on any set X is X*-proper. In a subsequent paper, we show how to construct T-proper left adequate monoids from any monoid T acting via order-preserving maps on a semilattice with identity, and prove that the free left adequate monoid is of this form. An alternative description of the free left adequate monoid will appear in a paper of Kambites. We show how to obtain the labeled trees appearing in his result from our structure theorem. Our results apply to the wider class of left Ehresmann monoids, and we give them in full generality. We also indicate how to obtain some of the analogous results in the two-sided case. This paper and its sequel, and the two of Kambites on free (left) adequate semigroups, demonstrate the rich but accessible structure of (left) adequate semigroups and monoids, introduced with startling insight by Fountain some 30 years ago. </jats:p
Smarandache U-liberal semigroup structure
No full textIn this paper, Smarandache U-liberal semigroup structure is given. It is shown that
a semigroup S is Smarandache U-liberal semigroup if and only if it is a strong semilattice of some rectangular monoids. Consequently, some corresponding results on normal orthocryptous semigroups and normal orthocryptogroups are generalized and extended
Diffusive author(s), cohesive author: Analysis of S/N (1994)
No full textThis study indicates the ways in which various aspects of the author(s) are brought forth in Dumb type’s performance art, the S/N production. Previous research has suggested a non-hierarchical organization of Dumb type and the absence of a “privileged author” in Dumb type’s collaborative work, S/N. However, the results that I have investigated from member’s interviews on the creative process of S/N along with my analysis of the recorded images of S/N, indicate a different aspect of the author(s). First, S/N was created through, so to speak, the collective ideas of the members of Dumb type. Further, S/N has at least nine quotations from previous performances, installations, and printed writings, besides the work-in-progress technique. Explicating one of the “author functions” as given by Michel Foucault, each text has plural subjects of the author. However, it has been revealed from members’ interviews that Teiji Furuhashi had a decision-making role in selecting the members’ ideas within the performance. Since then, S/N has had plural subjects of creation; however, Furuhashi is one of the subjects of creation along with the “privileged author.” S/N has plural authors (diffusive authors) yet at the same time, it has a “privileged author,” Teiji Furuhashi (cohesive author)
Going Beyond Counting First Authors in Author Co-citation Analysis
No full textThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Dispelling the Myths Behind First-author Citation Counts
No full textWe conducted a full-scale evaluative citation analysis study of scholars in the XML research field to explore just how different from each other author rankings resulting from different citation counting methods actually are, and to demonstrate the capability of emerging data and tools on the Web in supporting more realistic citation counting methods. Our results contest some common arguments for the continued
use of first-author citation counts in the evaluation of scholars, such as high correlations between author rankings by first-author citation counts and other citation
counting methods, and high costs of using more realistic citation counting methods that are not well-supported by the ISI databases. It is argued that increasingly available digital full text research papers make it possible for citation analysis studies to go beyond what the ISI databases have directly supported and to employ more
sophisticated methods
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